Math Problem Statement

Which angles are alternate interior angles in the given diagram, where lines JL and MO are parallel, and a transversal INP crosses them?

Solution

In the given diagram, lines JL\overleftrightarrow{JL} and MO\overleftrightarrow{MO} are parallel, and the transversal INP\overleftrightarrow{INP} crosses them at points KK and NN, respectively.

Alternate interior angles are angles that:

  1. Are on opposite sides of the transversal.
  2. Lie between the two parallel lines.

Looking at the diagram:

  • JKN\angle JKN is on the top side of the transversal between the two parallel lines.
  • ONK\angle ONK is on the opposite side of the transversal but also between the two parallel lines.

Thus, the correct pair of alternate interior angles is:

JKN\angle JKN and ONK\angle ONK.

The correct answer is the first option.

Would you like more details or have any questions?

Here are five related questions:

  1. What are corresponding angles, and can you identify any from this diagram?
  2. How can you identify other pairs of alternate interior angles in different configurations?
  3. What are the properties of parallel lines when intersected by a transversal?
  4. Can two angles formed by a transversal be supplementary? Which pairs are supplementary here?
  5. How can alternate exterior angles be identified in a diagram like this?

Tip: Remember, alternate interior angles are always congruent when the lines are parallel.

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Transversal
Alternate Interior Angles

Formulas

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Theorems

Alternate Interior Angles Theorem

Suitable Grade Level

Grades 6-8